Purpose. In interocular suppression, a suprathreshold target presented monocularly (to target-eye) can be rendered invisible by a salient competitor presented to the other eye (competitor-eye). Here we develop and test a computational model of interocular suppression and distinguish the role of feature-based and eye-based attention. Psychophysics. Observers performed an orientation-discrimination task on a small (1.5º diameter) monocular target, either presented alone or simultaneously with one of several competitors. The size and eye-of-origin of the competitors were manipulated. Three competitors–small (1.5º), medium (2.5º) and large (8º)–were presented to the competitor-eye. To disentangle feature-based and eye-based attention, large split competitor (8º) was segmented into two regions: the center (same as the small competitor) was presented to the competitor-eye whereas the surround was presented to the target-eye. Target contrast varied from trial-to-trial randomly, and competitor contrast was fixed at 23%. We measured psychometric functions: d’ vs. target contrast. Computational model. Two processes contributed to the strength of interocular suppression. According to the model, the salient competitor induced an exogenous attentional modulation selective for the location and orientation of the competitor, thereby increasing the gain of the responses to the competitor and reducing the gain of the responses to the target. Additional suppression was induced by divisive normalization, similar to other forms of visual masking. Results. Small and medium competitors induced a response-gain change for responses to the target (consistent with Ling & Blake, 2012). But large competitors induced a contrast-gain change, even when the competitor was split between the two eyes. The model correctly predicted these results and outperformed an alternative model in which the attentional modulation was eye specific. Conclusion. Both exogenous attention (selective for feature and location) and divisive normalization contribute to interocular suppression.